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19
Simple easy terms
 Intersection Types and Related Systems, volume 70 of Electronic Notes in Computer Science
, 2002
"... Dipartimento di Informatica Universit`a di Venezia ..."
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Cited by 13 (3 self)
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Dipartimento di Informatica Universit`a di Venezia
Intersection Types and Lambda Models
, 2005
"... Invariance of interpretation by #conversion is one of the minimal requirements for any standard model for the #calculus. With the intersection type systems being a general framework for the study of semantic domains for the #calculus, the present paper provides a (syntactic) characterisation of t ..."
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Cited by 11 (1 self)
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Invariance of interpretation by #conversion is one of the minimal requirements for any standard model for the #calculus. With the intersection type systems being a general framework for the study of semantic domains for the #calculus, the present paper provides a (syntactic) characterisation of the above mentioned requirement in terms of characterisation results for intersection type assignment systems.
Two behavioural lambda models
 Types for Proofs and Programs
, 2003
"... Abstract. We build a lambda model which characterizes completely (persistently) normalizing, (persistently) head normalizing, and (persistently) weak head normalizing terms. This is proved by using the finitary logical description of the model obtained by defining a suitable intersection type assign ..."
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Abstract. We build a lambda model which characterizes completely (persistently) normalizing, (persistently) head normalizing, and (persistently) weak head normalizing terms. This is proved by using the finitary logical description of the model obtained by defining a suitable intersection type assignment system.
Reducibility: a ubiquitous method in lambda calculus with intersection types
, 2002
"... A general reducibility method is developed for proving reduction properties of lambda terms typeable in intersection type systems with and without the universal type #. Sufficient conditions for its application are derived. This method leads to uniform proofs of confluence, standardization, and weak ..."
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Cited by 5 (2 self)
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A general reducibility method is developed for proving reduction properties of lambda terms typeable in intersection type systems with and without the universal type #. Sufficient conditions for its application are derived. This method leads to uniform proofs of confluence, standardization, and weak head normalization of terms typeable in the system with the type #. The method extends Tait's reducibility method for the proof of strong normalization of the simply typed lambda calculus, Krivine's extension of the same method for the strong normalization of intersection type system without #, and StatmanMitchell's logical relation method for the proof of confluence of ##reduction on the simply typed lambda terms. As a consequence, the confluence and the standardization of all (untyped) lambda terms is obtained.
Intersection Types and Lambda Theories
 International Workshop on Isomorphisms of Types
, 2002
"... We illustrate the use of intersection types as a semantic tool for showing properties of the lattice of ltheories. Relying on the notion of easy intersection type theory we successfully build a filter model in which the interpretation of an arbitrary simple easy term is any filter which can be desc ..."
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We illustrate the use of intersection types as a semantic tool for showing properties of the lattice of ltheories. Relying on the notion of easy intersection type theory we successfully build a filter model in which the interpretation of an arbitrary simple easy term is any filter which can be described in an uniform way by a recursive predicate. This allows us to prove the consistency of a wellknow ltheory: this consistency has interesting consequences on the algebraic structure of the lattice of ltheories.
Characterising Strong Normalisation for Explicit Substitutions
 In Proceedings of Latin American Theoretical Informatics (LATIN'02), 2002. In Proceedings of Latin American Theoretical Informatics (LATIN'02), Canc
, 2002
"... Abstract. We characterise the strongly normalising terms of a compositionfree calculus of explicit substitutions (with or without garbage collection) by means of an intersection type assignment system. The main novelty is a cutrule which allows to forget the context of the minor premise when the c ..."
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Abstract. We characterise the strongly normalising terms of a compositionfree calculus of explicit substitutions (with or without garbage collection) by means of an intersection type assignment system. The main novelty is a cutrule which allows to forget the context of the minor premise when the context of the main premise does not have an assumption for the cut variable.
Normalisation is Insensible to λterm Identity or Difference
"... This paper analyses the computational behaviour of λterm applications. The properties we are interested in are weak normalisation (i.e. there is a terminating reduction) and strong normalisation (i.e. all reductions are terminating). One can prove that the application of a λterm M to a fixed number ..."
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This paper analyses the computational behaviour of λterm applications. The properties we are interested in are weak normalisation (i.e. there is a terminating reduction) and strong normalisation (i.e. all reductions are terminating). One can prove that the application of a λterm M to a fixed number n of copies of the same arbitrary strongly normalising λterm is strongly normalising if and only if the application of M to n different arbitrary strongly normalising λterms is strongly normalising. I.e. one has that M X
Recursive Domain Equations of Filter Models
 In SOFSEM 2008, LNCS 4910
, 2008
"... Abstract. Filter models and (solutions of) recursive domain equations are two different ways of constructing lambda models. Many partial results have been shown about the equivalence between these two constructions (in some specific cases). This paper deepens the connection by showing that the equ ..."
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Abstract. Filter models and (solutions of) recursive domain equations are two different ways of constructing lambda models. Many partial results have been shown about the equivalence between these two constructions (in some specific cases). This paper deepens the connection by showing that the equivalence can be shown in a general framework. We will introduce the class of disciplined intersection type theories and its four subclasses: natural split, lazy split, natural equated and lazy equated. We will prove that each class corresponds to a different recursive domain equation. For this result, we are extracting the essence of the specific proofs for the particular cases of intersection type theories and making one general construction that encompasses all of them. This general approach puts together all these results which may appear scattered and sometimes with incomplete proofs in the literature. 1
Compositional Characterisations of λterms using Intersection Types
, 2003
"... We show how to characterise compositionally a number of evaluation properties of λterms using Intersection Type assignment systems. In particular, we focus on termination properties, such as strong normalisation, normalisation, head normalisation, and weak head normalisation. We consider also the p ..."
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We show how to characterise compositionally a number of evaluation properties of λterms using Intersection Type assignment systems. In particular, we focus on termination properties, such as strong normalisation, normalisation, head normalisation, and weak head normalisation. We consider also the persistent versions of such notions. By way of example, we consider also another evaluation property, unrelated to termination, namely reducibility to a closed term. Many of these characterisation results are new, to our knowledge, or else they streamline, strengthen, or generalise earlier results in the literature. The completeness parts of the characterisations are proved uniformly for all the properties, using a settheoretical semantics of intersection types over suitable kinds of stable sets. This technique generalises Krivine's and Mitchell's methods for strong normalisation to other evaluation properties.